Problem Solving

BTGmoderatorLU wrote: ↑

Sat Jun 27, 2020 3:06 pm

Source: Manhattan Prep

Narcisse and Aristide have numbers of arcade tokens in the ratio 7:3, respectively. Narcisse gives Aristide some of his tokens, and the new ratio is 6;5. What is the least number of tokens that Narcisse could have given to Aristide?

A. 9
B. 17
C. 21
D. 27
E. 53

The OA is B

Solution:

Let 7n and 3n be the number of tokens Narcisse and Aristide respectively had originally and x be the number of tokens Narcisse gave to Aristide. We can create the equation:

(7n - x) / (3n + x) = 6/5

6(3n + x) = 5(7n - x)

18n + 6x = 35n - 5x

11x = 17n

x = 17n/11

Since 17 is not divisible by 11, we see that the least positive value of n is 11. Therefore, the least positive value of x is 17(11)/11 = 17.

Answer: B